Question

(tanx)^[1/(cosx-sinx)]当x趋于π/4时，求极限

(tanx)^[1/(cosx-sinx)]当x趋于π/4时，求极限

Answer 1

简单计算一下即可，答案如图所示

Answer 2

原式=lim(x趋于π/4）e^[lntanx/(cosx-sinx)]
…………分子
分母
同时趋于0，罗必达法则
=lim(x趋于π/4）e^[(1/cos^2xtanx)/(-sinx-cosx)]
=lim(x趋于π/4）e^1/[-sinxcosx(sinx+cosx)]
=e^(-√2)